Lee Minie Balls

[Underclocked]

Yes and yes.  You might have someone with a lathe turn down the core pin so as to yield a bullet with a thicker skirt.  The thin skirt flies well with lighter charges but you can go to a better hunting charge if the skirt is thicker.  If you do that, only narrow the cone section and nothing else.

Lube 'em up with Crisco and fill the base with same.

[Underclocked]

Hmm, I did mine myself and kind of butchered it as I didn't have a lathe but I would recommend you go for at least .1" minimum skirt thickness.  Lube the grooves and cup on the bullet.

I've a friend in Hawaii that did this (but a machinist did his work) and he sent me some truly excellent bullets from his mold.   He went for .1" minimum skirt but got just a shade over that.  I don't think you could really go wrong if you were to near completely remove that base cone so long as it's evenly done.

You can drill out the holder for that cone piece and then pop rivet it back in place so long as you keep the hole small.  If it's a wee bit loose afterwards, don't worry about it as it should self-center.  The vital thing is not to take anything off the flat part of the piece.